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# Analytical geometry

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### Analytical geometry

1. 1. ANALYTICAL GEOMETRY SJ van Heerden 09/03/2014
2. 2. HISTORY Introduced in the 1630s Aided the development of calculus RENE DESCARTES (1596-1650) and PIERRE DE FERMAT (1601-1665), French mathematicians, independently developed the foundations for analytical geometry
3. 3. CARTESIAN PLANE
4. 4. • x-axis (horizontal axis) where the x values are plotted along. • y-axis (vertical axis) where the y values are plotted along. • origin, symbolized by 0, marks the value of 0 of both axes • coordinates are given in the form (x,y) and is used to represent different points on the plane.
5. 5. Slope of a Line
6. 6. Slope of a Line
7. 7. Slope of a Line
8. 8. Slope of a Line
9. 9. Slope of a Line
10. 10. Inclination of a Line y y L L θ O M x θ O M x
11. 11. Angle between Two Lines
12. 12. Angle between Two Lines • If θ is angle, measured counter-clockwise, between two lines, then • where m2 is the slope of the terminal side and m1 is the slope of the initial side
13. 13. SLOPE OF PARALLEL LINES
14. 14. SLOPE OF PERPENDICULAR LINES
15. 15. Sample Problems
16. 16. EQUATION OF A CIRCLE
17. 17. EQUATION OF CIRCLE (origin is not the center) A (h, k) B ( x, y)
18. 18. Graph the following circle.
19. 19. REFERENCES - Demirdag, M. (2013). Analytic geometry [PowerPoint Presentation]. Available at: http://www.slideshare.net/mstfdemirdag/analytic-geometry-8693115. Accessed on: 4 March 2014 - Felipe, N, M. (2013). Analytic geometry basic concepts [PowerPoint Presentation]. Available at: http://www.slideshare.net/NancyFelipe1/analytic-geometry-basic-concepts.Accessed on: 4 March 2014 - Marasigan, D. (2013). Lecture #2 analytic geometry [PowerPoint Presentation]. Available at: http://www.slideshare.net/denmarmarasigan/lecture-2-analytic-geometry.Accessed on: 4 March 2014 - Marasigan, D. (2013). Lecture #3 analytic geometry [PowerPoint Presentation]. Available at: http://www.slideshare.net/denmarmarasigan/lecture-3-analytic-geometry.Accessed on: 4 March 2014 - Marasigan, D. (2013). Lecture #5 analytic geometry [PowerPoint Presentation]. Available at: http://www.slideshare.net/denmarmarasigan/lecture-5-analytic-geometry. Accessed on: 4 March 2014